Macroeconometrics Project
Summary
Motivation:
The purpose of this course is to get a theoretical and practical understanding of empirical methods for business cycle analysis and forecasting. The two main classes of models used for this purpose in research and policy environments alike are the Dynamic Factor Model (DFM) and Vector Autoregressions (VAR). Accordingly, I aim to conduct a simple exercise where I compare the forecasting performance of these two popular models for the real GDP growth of the euro area. In particular, I will use similar versions of the models where I have mixed frequencies (i.e., low frequency of quarterly and high frequency of monthly) and an unbalanced panel of data (i.e., ragged edges). Further, I specify the same small-to-medium-size model (between 6 and 15 variables) for both models and perform estimation using Bayesian techniques. The models will be similar in spirit to Camacho and Perez-Quiros (2010) for the DFM and to Schorfheide and Song (2015) for the VAR.
The analysis will consist of providing point and density forecasts (i.e., median and percentiles of the posterior distribution) for the euro area real GDP growth over the short term. Then, I will contrast the forecasting ability of these two models by comparing them with the ECB official macroeconomic projections for the euro area growth (i.e., the ECB projections are conducted using a suite of state-of-the-art models, so it is a challenging benchmark to beat). Finally, I will compare the in-sample forecast performance of the models (compare the RMSE).
This exercise will shed light on whether there are relevant differences between the DFMs and VARs in terms of forecasting and whether they are able to provide similar growth forecasting profiles as the ones from professional models used in the ECB to conduct macroeconomic projections.
Scope:
Target
- Euro area real GDP growth
Models
- Mixed-frequency Bayesian DFM with unbalanced panel
- Mixed-frequency Bayesian VAR with unbalanced panel
Analysis
- Point and density forecasts of target variable
- Comparison to ECB Dec-2023 BMPE and Mar-2024 MPE
- Forecast performance comparison between models (in-sample forecasts)
Specification:
Dynamic Factor Model (e.g., Q=1, M=2)
Model:
State-space representation:
Note: For Bayesian estimation we rewrite the model as a linear regression in that we include the dynamics (i.e., autoregressive polynomial) of the idiosyncratic component in the measurement equation. Further, for simplicity we assume no idiosyncratic dynamics of the quarterly/low-frequency target variable.
Vector Autoregression (e.g., Q=1, M=2)
Model:
=
.State-space representation:
Note: For Bayesian estimation the series enter in (log) levels since we assume a Minnesota-type prior with the variables following a random walk.
References
Camacho, Maximo, and Gabriel Perez‐Quiros. "Introducing the euro‐sting: Short‐term indicator of euro area growth." Journal of Applied Econometrics 25, no. 4 (2010): 663-694.
Schorfheide, Frank, and Dongho Song. "Real-time forecasting with a mixed-frequency VAR." Journal of Business & Economic Statistics 33, no. 3 (2015): 366-380.
@Erik Andres Escayola
Main script
Data description
(Mnemonic -> Variable - Sector - Type - Frequency)
1 GDP -> Real GDP - Activity - Hard - Q
2 PMI -> Composite output PMI - Activity - Soft - M
3 ESI -> Economic sentiment - Activity - Soft - M
4 IP -> Industrial production manufacturing - Activity - Hard - M
5 RS -> Retail sales - Activity - Hard - M
6 EMP -> Unemployment rate - Activity - Hard -M
7 EEXP-> Extra-euro area exports - Activity - Hard - M
8 CPI -> Consumer prices - Prices - Hard - M
9 REER-> Real effective exchange rate - Prices - Hard - M
10 COM -> Commodity spot aggregate - Prices - Hard - M
11 CISS-> Sovereign stress - Financial - Hard/Soft - M
12 EQTY-> EURO STOXX 50 - Financial - Hard - M
13 INT -> Short-term interest rate & shadow rate - Financial - Hard/Soft - M
14 EPU -> Economic policy uncertainty - Other - Soft - M
15 SBI -> Supply-bottleneck - Other - Soft - M
Note: always put quarterly variables first
Housekeeping
Data loading and wrangling
Enter data file name:
Select variables:
Select upper bound credible band:
Preprocess data:
Model estimation
Gibbs sampler draws:
Estimate DFM:
Estimate VAR:
Comparison analysis wrt ECB projections
Enter ECB projections file name:
Select specs:
Run comparison with latest ECB projections:
Comparison analysis between models
Select specs:
Run expanding window forecast exercise:
Results report
Click on "Hide code" on the right of the "Live Editor" file to see results only.
Build the report (displaying code sections):